The class of weak $w$-projective modules is a precover
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Let $R$ be a commutative ring with identity. Denote by $\wp$ the class of weak $w$-projective $R$-modules and by $\wp^{\bot}$ the right orthogonal complement of $\wp$. It is shown that $(\wp,\wp^{\bot})$ is a hereditary and complete cotorsion theory, and so every $R$-module has a special weak $w$-projective precover. We also give some necessary and sufficient conditions for weak $w$-projective modules to be $w$-projective. Finally it is shown that when we discuss the existence of a weak $w$-projective cover of a module, it is enough to consider the $w$-envelope of the module.
Abstract
Let $R$ be a commutative ring with identity. Denote by $\wp$ the class of weak $w$-projective $R$-modules and by $\wp^{\bot}$ the right orthogonal complement of $\wp$. It is shown that $(\wp,\wp^{\bot})$ is a hereditary and complete cotorsion theory, and so every $R$-module has a special weak $w$-projective precover. We also give some necessary and sufficient conditions for weak $w$-projective modules to be $w$-projective. Finally it is shown that when we discuss the existence of a weak $w$-projective cover of a module, it is enough to consider the $w$-envelope of the module.
참고문헌 (14)
- F. A. A. Almahdi, "On the right orthogonal complement of the class of w-flat modules", J. Ramanujan Math. Soc, 33(2), pp.159~175 (2018)
- P. C. Eklof, "How to make Ext vanish", Bull. London Math. Soc, 33(1), pp.41~51 (2001)[DOI]
- E. E. Enochs, "De Gruyter Expositions in Mathematics" (2000), Walter de Gruyter & Co
- HWANKOO KIM, "ON LCM-STABLE MODULES", Journal of Algebra and Its Applications, 13(04), pp.1350133~ (2014), World Scientific Pub Co Pte Lt[DOI]
- Y. Y. Pu, "w∞-projective modules and Krull domains", Commun. Algebra
- Y. Y. Pu, "w∞-Warfield cotorsion modules and Krull domains", Algebra Colloq
- J. Trlifaj, "Covers, envelopes, and cotorsion theories", Lecture notes for the workshop, Homological Methods in Module Theory (2000)
- F. Wang, "On w-projective modules and w-flat modules", Algebra Colloq, 4(1), pp.111~120 (1997)
- F. Wang, "Two generalizations of projective modules and their applications", J. Pure Appl. Algebra, 219(6), pp.2099~2123 (2015)[DOI]
- Fanggui Wang, "Foundations of Commutative Rings and Their Modules", Algebra and Applications, 22 (2016), Springer Singapore[DOI]
- Fanggui Wang, "THE ω-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGS", 대한수학회보, 52(4), pp.1327~1338 (2015), 대한수학회
- Fanggui Wang, "A homological characterization of Krull domains II", Communications in Algebra, 47(5), pp.1917~1929 (2019), Informa UK Limited[DOI]
- F. Wang, "A new version of a theorem of Kaplansky", Comm. Algebra, 48(8), pp.3415~3428 (2020)[DOI]
- Fanggui Wang, "A homological characterization of Krull domains", 대한수학회보, 55(2), pp.649~657 (2018), 대한수학회